how to solve this question

Answer:

Step-by-step explanation:

To find the height of the rocket, we can use the tangent function. We know the angle of elevation (75°), the height of Homer's eyes (1.8 meters), and the distance from Homer to the rocket (8 meters), so we can use the formula:

tan(angle) = height / distance

We'll solve for the height:

height = distance * tan(angle)

height = 8 * tan(75°)

However, we need to convert the angle from degrees to radians first, as the tangent function operates in radians. We can use the formula:

radians = degrees * (π / 180)

radians = 75° * (π / 180) = 1.309 radians

Now, we can substitute the value for the angle in radians back into the original equation:

height = 8 * tan(1.309)

Using a calculator, we can find that the height is approximately 15.57 meters.

So, the height of the rocket is approximately 15.57 meters.

On solving the provided question we can say that 15 bags total 258.21 kilos in weight. 15 bags have a volume of 2.222 cubic yards.

A cuboid is a solid or three-dimensional form in geometry. A cuboid is a convex polyhedron having 8 vertices, 12 sides, and 6 rectangular faces. Another name for a cuboid is a cuboid. A cube is a cuboid with six square faces. Boxes include things like books and bricks. The following are the key variations between cubic and cubic: In contrast to a cube, which has rectangular faces, a cube has six equally sized square faces. Even though the cube and cuboid structures have a similar appearance, they differ in some ways in terms of side length, diagonal, and area.

In terms of dimensions, a pound is equivalent to 0.453 kilos and a cubic yard is equivalent to 27 cubic feet. We next continue to get the weight and volume of 15 bags using the conversions below:

weight

x = 15bags X 28/1 X 0.453

x = 258.21 kg

volume

x = 15 X 4/27 = 2.222 yd

15 bags total 258.21 kilos in weight. 15 bags have a volume of 2.222 cubic yards.

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On solving the provided question we can say that 15 bags total 258.21 kilos in weight. 15 bags have a volume of 2.222 cubic yards.

A cuboid is a solid or three-dimensional form in geometry. A cuboid is a convex polyhedron having 8 vertices, 12 sides, and 6 rectangular faces. Another name for a cuboid is a cuboid. A cube is a cuboid with six square faces. Boxes include things like books and bricks. The following are the key variations between cubic and cubic: In contrast to a cube, which has rectangular faces, a cube has six equally sized square faces. Even though the cube and cuboid structures have a similar appearance, they differ in some ways in terms of side length, diagonal, and area.

In terms of dimensions, a pound is equivalent to 0.453 kilos and a cubic yard is equivalent to 27 cubic feet. We next continue to get the weight and volume of 15 bags using the conversions below:

weight

x = 15bags X 28/1 X 0.453

x = 258.21 kg

volume

x = 15 X 4/27 = 2.222 yd

15 bags total 258.21 kilos in weight. 15 bags have a volume of 2.222 cubic yards.

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The perimeter of the triangle is equal to 28.7 using the trigonometric ratio

The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths. The basic trigonometric ratios includes;

sine, cosine and tangent.

tan60 = q/4 {opposite/adjacent}

q = 4 × tan60 {cross multiplication}

q = 6.9282

sin60 = q/r {opposite/hypotenuse}

sin60 = 6.9282/r

r = 6.9282/sin60 {cross multiplication}

r = 8

sin45 = q/s {opposite/hypotenuse}

sin45 = 6.9282/s

s = 6.9282/sin45 {cross multiplication}

s = 9.8

cos45 = p/s {adjacent/hypotenuse}

cos45 = p/9.8

p = 6.9282 {cross multiplication}

perimeter of the triangle = 4 + p + s + r

perimeter of the triangle = 4 + 6.9282 + 9.8 + 8

perimeter of the triangle = 28.7282

Therefore, the perimeter of the triangle is equal to 28.7 using the trigonometric ratio.

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Answer:

The slope of line 1 is -4/3.

The slope of line 2 is 2/3.

Line 1 is neither parallel nor perpendicular to line 2.

Step-by-step explanation:

firstly we find slope using two point formula .

The lines are said to be parallel when their slopes are equal.The lines are said to be perpendicular when the product of their slope is -1. Hence, line 1 is neither parallel nor perpendicular to line 2.

The value of the fifth term B is 17.

An ordered list of things is a sequence (or events). Similar to a set, it has members (also called elements, or terms). The length of the sequence is the number of ordered items (potentially infinite).

Given:

The first term of the sequence is 2.

a₁ = 2

And the explicit formula of the sequence,

aₙ = (-2)aₙ₋₁ + 3.

The value of a₂:

a₂ = (-2)a₁+ 3.

a₂ = -2(2) + 3 = -1

And a₃ = -2(-1) + 3 =5

a₄ = -2(5) + 3 = -7

Now, the value of the fifth term,

a₅ = -2(-7) + 3 = 17.

Therefore, the fifth term is 17.

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a) The required margin of error and lower and upper limits are:-

E =0.124

Lower limit =3.026

Upper limit =  3.274

b) sample size is n = 27.

An estimated range for an unknown parameter is known as a confidence interval. The 95% confidence level is the most popular, however other levels, such as 90% or 99%, are occasionally used when computing confidence intervals.

The margin of error will be calculated as:-

a) Margin of error (E) :

[tex]E = Z_c\times \dfrac{\sigma}{\sqrt{n}}[/tex]

E =0.124

Margin of error = E =0.124

The lower and upper limits are calculated as:-

Lower limit = x-E

L= 3.15 - 0.124

L= 3.026

Lower limit =3.026

Upper limit = x + E

U= 3.15 + 0.124

U= 3.274

Upper limit =  3.274

b) The following equation may be used to calculate the right number of samples, n when is already known:

Margin of error = 0.13

Sample size (n):

[tex]n = (\dfrac{Z_c\sigma}{E})^2[/tex]

[tex]n = (\dfrac{1.28\times 0.36}{0.09})^2[/tex]

n = 26.21

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We can represent the sinusoidal function for Tarzan's motion as given below.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Given is that Tarzan is swinging back and forth on his grapevine. As he swings, he goes back and forth across the riverbank, going alternately over land and water. Jane decides to model mathematically his motion and starts her stopwatch.

Assume the sinusoidal equation to be -

y = Asin(ωt)

We can represent the coordinates as -

For {t} = 2, {y} = -23. So -

- 23 = Asin(2ω)                                                    ... { 1 }

For {t} = 5, {y} = 17. So -

17 = Asin(5ω)                                                       ... { 2 }

Therefore, we can represent the sinusoidal function for Tarzan's motion as given above.

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Answer:

Step-by-step explanation:

22

The direction of the sum of the two vectors is along the west direction

Assuming vector A is pointing west ward and vector B is pointing eastward

The direction of vector A to the horizontal is negative solved by

= -6 cos 30

= -5.196

Adding both vectors

= vector A + vector B

= -5.196 + 5

= -0.196

Hence the direction is to the west since it is negative

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Answer:258 containers

Step-by-step explanation:

Simply,

16770/65=258.

Hope this helps :]

Answer:A decrease of 20%.

First we must subtract out new total from our old total.

9390 - 7512 is 1878. This means that there is a difference of 1878. Next we must divided both 7512 and 1878 into 9390.

7512/9390 is 0.8 & 1878/9390 is 0.2

As a percentage that is 80% and 20%.

This means that the new amount of sugar only makes up 80% of the old amount. That means that there was a decrease of 20% of kilograms of sugar.

I hope this helped & Good Luck <3 !!!

The potential energy of the roller coaster car at the top of a hill is 661,068.8 J.

The correct answer choice is option D

Potential energy is a form of energy which is dependent on the relationship between different system components.

The gravitational constant, g = 9.8 m/s².

Mass, m = 1088 grams

Height, h = 62 meters

So, The amount of potential energy the car has;

PE = mgh.

PE = 1088 × 9.8 × 62

PE = 661,068.8J

Ultimately, the car has a potential energy of 661,068.8J.

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Answer:

8.25 gallan=33 quart

Step-by-step explanation:

From  transitive property of equality, RT = SU.

Given:

RS = TU

What is Segment addition postulate  ?

The segment addition postulate states that if we are given two points on a line segment, A and C, a third point B lies on the line segment AC if and only if the distances between the points meet the requirements of the equation AB + BC = AC

Since , from Segment addition postulate

ST = ST

What is addition property of equality ?

The addition property of equality tells us that adding the same number to each side of an equation gives us an equivalent equation. if a-b=c,then a−b+b=c+b, or a=c+b. The same goes with the subtraction property of equality.

Now , by addition property of equality

SU = ST + TU

Similarly,

RT = RS + ST

Now , Using transitive property of equality,

RT = SU

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The volume of this cylinder is 1.5 times that of the cone. The cylinder volume is 452.4 in³ while the cone volume is 301.6 in³

An equation is an expression that shows how numbers and variables are linked together using mathematical operations such as addition, subtraction, multiplication and division.

A cylinder and a cone have the same diameter: 8 inches. The height of the cylinder is 9 inches. The height of the cone is 18 inches.

Radius of cone/cylinder = diameter/2 = 8 in/2 = 4 in.

Volume of cylinder = π * radius² * height = π * (4)² * 9 = 452.4 in³

Volume of cone = (1/3) * π * radius² * height = (1/3) * π * (4)² * 18 = 301.6 in³

The volume of this cylinder is 1.5 times that of the cone

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The given expression simplifies to sin 2x.

Option (D) is correct.

What are trigonometric ratios?

Trigonometric ratios are ratios of the sides of a right triangle that are used to define the relationships between the angles and the sides of the triangle. The three basic trigonometric ratios are sine, cosine, and tangent, which are commonly abbreviated as sin, cos, and tan, respectively.

The expression (sin 3x)(cos x) − (cos 3x)(sin x) is an example of a trigonometric identity known as the "sin of a difference" formula:

sin(A - B) = sin A cos B - cos A sin B

By comparing this formula to the given expression, we can see that:

A = 3x

B = x

Substituting these values into the formula, we get:

sin(3x - x) = sin 2x = (sin 3x)(cos x) − (cos 3x)(sin x)

Hence, the given expression simplifies to sin 2x.

Option (D) is correct.

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Answer:

x=4

Step-by-step explanation:

-6x = -6-18

-6x = -24

-6x/-6 = -24/-6

x =4

On solving the provided question, we can say that first angle is 37.9° . second angle will be 52.1°.

An angle is a fοrm in Euclidean geometry made composed of two rays, called the angle's sides, that meet at a pοint in the middle known as the angle's vertex. In the plane where the rays are placed, twο rays can produce an angle.

An angle is alsο produced when two planes intersect. They're knοwn as dihedral angles. In plane geοmetry, an angle is the form that two rays or lines with a commοn termination might take. The Latin word "angulus," which means "hοrn," is where the English word "angle" comes from. The two rays, also knοwn as the sides of the angle, have a common termination knοwn as the vertex.

x = first angle

Complementary angle is 14.2 degrees more than the cοmplementary angle.

First angle  = x

Second angle = x + 14.2°

Complementary angle

x+x+14.2=90

2x+14.290

2x 90 14.2

2x = 75.8 x = 37.9

First angle is 37.9°.

Second angle will be:

x+14.2°

⇒37.9°+ 14.2°

⇒52.1°

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Answer:

cost of couch: $846

cost of coffee table: $282

Step-by-step explanation:

The number of positive integers that satisfy the conditions is 4

The positive integers are the natural numbers or also called counting numbers. These integers are also sometimes denoted by Z+. The positive integers lie on the right side of 0 on a number line. Z+ → 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25,

To satisfy positive integers that will have sum of four with a 1, a 2 or a 3

The integers are

13

31

112

211

therefore there are only 4 positive integers that have sum of 4 with a 1 , a 2 and a3

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The coordinates that lie on the equation of line y = 1 - 2x are P ( -3 , 7 ) and Q ( 6, -11)

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be P ( -3 , 7 )

Let the second point be Q ( 6 , -11 )

The equation of line is y = 1 - 2x

Substituting the values of x and y in the equation , we get

when x = -3

y = 1 - 2 ( -3 )

y = 1 + 6

y = 7

when x = 6

y = 1 - 2 ( 6 )

y = 1 - 12

y = -11

Hence , the coordinates of the equation of line are P ( -3 , 7 ) and Q ( 6, -11 )

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Answer:

280 calories and 12 grams of dietary fiber

Step-by-step explanation:

because 210(2/3) = 140

= 140 ÷ 1/2 = 280

we do the same steps with grams

9(2/3) = 6

= 6 ÷ 1/2 = 12

Answer:

(3) 3

Step-by-step explanation:

An arithmetic sequence is a sequence of numbers in which each of them can be defined by adding a common difference to a term to find the next term.

So for example, let the first term, or number be expressed as: [tex]a_1[/tex] and the common difference be expressed as: [tex]d[/tex] That means the second term, or number can be defined as: [tex]a_2=a_1+d[/tex]. If we now add the common difference to the second term, we would get the third term, and so on.

An arithmetic sequence can be compared to that of a linear equation, except it's a sequence of numbers... and also it's restricted to integers greater than zero (starts at first term, second term.... and so on)

So the common difference can be compared to the slope, and we can actually just use the slope formula! The "x" value being the term number, and the "y" value being the term. So the first term in the sequence is 5 can be expressed as: (1, 5) and the fifth term is 17 can be expressed as (5, 17). Now using the slope formula we would get: [tex]d=\frac{17-5}{5-1}=\frac{12}{4}=3[/tex]

Another way to think of it is the first term is 5, and if we add "d" or the common difference to it, we get the second term, if we add another "d" we get the third term, if we another "d" we get the fourth term and if add yet another "d" we get the fifth term. We add a total of four "d's" which can be expressed as: [tex]5+4d[/tex] and this equals the fifth term, but we also know this to be equal to 17, so we can set them equal to each other: [tex]5+4d=17[/tex] now just subtract 5 and divide by 4 to get: [tex]d=3[/tex]

Answer:

you su ck hah lol

Step-by-step explanation:

ez

- 54  is the value of x in the linear equation .

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                               Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

f(X) =  x² + 7x - 4

A) f(-2) + f(4) = - 14 + 40  = 26

B) f(-2) - f(4) =  - 14 - 40  = -54

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y=mx+b

m=slope

b= y-intercept

x=6

y=-5

-5= -1/3(6)+b

-5= 2+b

-2       -2

      -7    =  b

y= -1/3x-7

Answer:

y=-1/3x-3

Step-by-step explanation:

On solving the provided question, we can say that total volume of figure = total volume of cuboid = lbh =  18+24 = 32 in cubic

A cuboid is a solid or three-dimensional form in geometry. A cuboid is a convex polyhedron having 8 vertices, 12 sides, and 6 rectangular faces. Another name for a cuboid is a cuboid. A cube is a cuboid with six square faces. Boxes include things like books and bricks. The following are the key variations between cubic and cubic: In contrast to a cube, which has rectangular faces, a cube has six equally sized square faces. Even though the cube and cuboid structures have a similar appearance, they differ in some ways in terms of side length, diagonal, and area.

volume of figure 1 = volume of cuboid = lbh = 8*3*1 = 24 in cubic

volume of figure 2= volume of cuboid = lbh = 6*3*1 = 18 in cubic

total volume of figure = total volume of cuboid = lbh =  18+24 = 32 in cubic

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On solving the provided question, we can say that total volume of figure = total volume of cuboid = lbh =  18+24 = 32 in cubic

In geometry, a cuboid is a solid or three-dimensional form. A cuboid is an 8-vertex, 12-sided polyhedron with 6 rectangular faces. A cuboid is another name for a cuboid. A cube is a six-square-faced cuboid. Books and bricks are examples of items found in boxes. The key distinctions between cubic and cubic are as follows: A cube has six equally sized square faces, as opposed to a cube's rectangular faces. Although the cube and cuboid structures appear similar, they differ in terms of side length, diagonal, and area.

Figure 1 volume = cuboid volume = lbh = 8*3*1 = 24 in cubic

Figure 2 volume = cuboid volume = lbh = 6*3*1 = 18

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A. The amount deducted from Frank's bank every years is $59700

B. The salary of the tax will be $99500.

C. Tax deducted from her new pay is $39800

A quick and simple way to figure out interest on money is to use the simple interest technique, which adds interest at the same rate for each time cycle and always to the initial principal amount. Any bank where we deposit our funds will pay us interest on our investment. One of the different types of interest charged by banks is simple interest. Now, before exploring the idea of basic curiosity in further detail,

a. 79600 - (79600 × 25%)

$59700

b. The formula for simple interest is:

S = p*t*r/100

p = 79600

r = 25%

t=1

S = 79600*1*25/100 = 19900

New salary = 79600 + 19900

= $99500

Hence the salary of the tax will be $99500.

c. 99500 - 59700

 = $39800

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